An encoder causally observes the Wiener process and decides when what to transmit about it. A decoder makes real-time estimation of using received codewords. We determine causal encoding decoding policies that minimize mean-square error, under long-term communication rate constraint R bits/s. show an optimal policy can be implemented as a sampling followed by compressing policy. prove samples o...

In the drug design process, one wants to construct chemical compounds with certain properties. In order to establish the mathematical basis for the connections between molecular structures and physicochemical properties of chemical compounds, some so-called structure-descriptors or ”topological indices” have been put forward. Among them, the Wiener index is one of the most important. A long sta...

For many products, it is not uncommon to see that a unit with a higher degradation rate has a more volatile degradation path. Motivated by this observation, we propose a new class of random effects model for the Wiener process model. We express the Wiener process in a special form and allow one of the parameters to be random across the product population so that a unit with a high degradation r...

In this paper, block-oriented systems with linear parts based on Laguerre functions is used to approximation of a cone crusher dynamics. Adaptive recursive least squares algorithm is used to identification of Laguerre model. Various structures of Hammerstein, Wiener, Hammerstein-Wiener models are tested and the MATLAB simulation results are compared. The mean square error is used for models val...

— In this paper, we propose an equivalent Wiener-Hopf equation. The proposed algorithm can obtain the weight vector of a TDL(tapped-delay-line) filter and the error simultaneously if the inputs are orthogonal to each other. The equivalent Wiener-Hopf equation was analyzed theoretically based on the MMSE(minimum mean square error) method. The results present that the proposed algorithm is equiva...

Fix ν > 0, denote by G(ν/2) a Gamma random variable with parameter ν/2 and let n ≥ 2 be a fixed even integer. Consider a sequence {F k } k≥1 of square integrable random variables belonging to the nth Wiener chaos of a given Gaussian process and with variance converging to 2ν. As k → ∞, we prove that F k converges in distribution to 2G(ν/2) − ν if and only if E(F 4 k) − 12E(F 3 k) → 12ν 2 − 48ν.

Closed solutions to the problem of pricing a Russian option when the stock is modeled by a diffusion with negative jumps are obtained. The Russian option is a perpetual American option on the maximum value of the stock. That stock is assumed to have the form of a Wiener process with drift and negative mixed–exponentially distributed jumps driven by a Poisson process. This result generalizes tho...

we focus on the use of two stable and accurate explicit finite difference schemes in order to approximate the solution of stochastic partial differential equations of it¨o type, in particular, parabolic equations. the main properties of these deterministic difference methods, i.e., convergence, consistency, and stability, are separately developed for the stochastic cases.